{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm import tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# for figure 8.7, run a simulation of 2 * @b steps\n",
    "def b_steps(b):\n",
    "    # set the value of the next b states\n",
    "    # it is not clear how to set this\n",
    "    distribution = np.random.randn(b)\n",
    "\n",
    "    # true value of the current state\n",
    "    true_v = np.mean(distribution)\n",
    "\n",
    "    samples = []\n",
    "    errors = []\n",
    "\n",
    "    # sample 2b steps\n",
    "    for t in range(2 * b):\n",
    "        v = np.random.choice(distribution)\n",
    "        samples.append(v)\n",
    "        errors.append(np.abs(np.mean(samples) - true_v))\n",
    "\n",
    "    return errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def figure_8_7():\n",
    "    runs = 100\n",
    "    branch = [2, 10, 100, 1000, 10000]\n",
    "    for b in branch:\n",
    "        errors = np.zeros((runs, 2 * b))\n",
    "        for r in tqdm(np.arange(runs)):\n",
    "            errors[r] = b_steps(b)\n",
    "        errors = errors.mean(axis=0)\n",
    "        x_axis = (np.arange(len(errors)) + 1) / float(b)\n",
    "        plt.plot(x_axis, errors, label='b = %d' % (b))\n",
    "\n",
    "    plt.xlabel('number of computations')\n",
    "    plt.xticks([0, 1.0, 2.0], ['0', 'b', '2b'])\n",
    "    plt.ylabel('RMS error')\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 100/100 [00:00<00:00, 5107.97it/s]\n",
      "  0%|          | 0/100 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 100/100 [00:00<00:00, 1515.64it/s]\n",
      "100%|██████████| 100/100 [00:00<00:00, 175.61it/s]\n",
      "100%|██████████| 100/100 [00:12<00:00,  8.11it/s]\n",
      "100%|██████████| 100/100 [13:57<00:00,  8.37s/it]\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure_8_7()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "rl",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.20"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
